Spin-polarization effects of an ultrarelativistic electron beam head-on colliding with an ultraintense two-color laser pulse are investigated comprehensively in the quantum radiation-dominated regime. We employ a Monte Carlo method, derived from the recent work of [Phys. Rev. Lett. 122, 154801 (2019)], to calculate the spinresolved electron dynamics and photon emissions in the local constant field approximation. We find that electron radiation probabilities in adjacent half cycles of a two-color laser field are substantially asymmetric due to the asymmetric field strengths, and consequently, after interaction the electron beam can obtain a total polarization of about 11% and a partial polarization of up to about 63% because of radiative spin effects, with currently achievable laser facilities, which may be utilized in high-energy physics and nuclear physics. Moreover, the considered effects are shown to be crucially determined by the relative phase of the two-color laser field and robust with respect to other laser and electron beam parameters.